\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\gdef\pointsofq@i{2}
\gdef\bonuspointsofq@i{0}
\gdef\pointsofq@ii{2}
\gdef\bonuspointsofq@ii{0}
\PgInfo{question@1}{1}
\PgInfo{question1@object1}{1}
\newlabel{question@1}{{1}{1}{Problems}{Item.6}{}}
\newlabel{firstpoints@onpage@1}{{1}{1}{Problems}{Item.6}{}}
\PgInfo{question@2}{1}
\PgInfo{question2@object1}{1}
\newlabel{question@2}{{2}{1}{Problems}{Item.7}{}}
\gdef\pointsofq@iii{3}
\gdef\bonuspointsofq@iii{0}
\gdef\pointsofq@iv{2}
\gdef\bonuspointsofq@iv{0}
\gdef\pointsofq@v{2}
\gdef\bonuspointsofq@v{0}
\gdef\pointsofq@vi{3}
\gdef\bonuspointsofq@vi{0}
\gdef\pointsonpage@i{14}
\gdef\pointsofq@vii{4}
\gdef\bonuspointsofq@vii{0}
\PgInfo{question@3}{2}
\PgInfo{question3@object1}{2}
\newlabel{question@3}{{3}{2}{Problems}{Item.8}{}}
\PgInfo{question@4}{2}
\PgInfo{question4@object1}{2}
\newlabel{question@4}{{4}{2}{Problems}{Item.9}{}}
\PgInfo{question@5}{2}
\PgInfo{question5@object1}{2}
\newlabel{question@5}{{5}{2}{Problems}{Item.10}{}}
\PgInfo{question@6}{2}
\PgInfo{question6@object1}{2}
\newlabel{question@6}{{6}{2}{Problems}{Item.11}{}}
\PgInfo{question@7}{2}
\PgInfo{question7@object1}{2}
\newlabel{question@7}{{7}{2}{Problems}{Item.12}{}}
\newlabel{firstpoints@onpage@2}{{7}{2}{Problems}{Item.12}{}}
\PgInfo{question@8}{2}
\PgInfo{question8@object1}{2}
\newlabel{question@8}{{8}{2}{Problems}{Item.13}{}}
\PgInfo{part@8@1}{2}
\PgInfo{question8@object2}{2}
\newlabel{part@8@1}{{a}{2}{Problems}{Item.14}{}}
\gdef\pointsofq@viii{3}
\gdef\bonuspointsofq@viii{0}
\gdef\pointsofq@ix{3}
\gdef\bonuspointsofq@ix{0}
\gdef\pointsofq@x{2}
\gdef\bonuspointsofq@x{0}
\gdef\pointsofq@xi{1}
\gdef\bonuspointsofq@xi{0}
\gdef\pointsofq@xii{2}
\gdef\bonuspointsofq@xii{0}
\gdef\pointsofq@xiii{2}
\gdef\bonuspointsofq@xiii{0}
\gdef\pointsofq@xiv{2}
\gdef\bonuspointsofq@xiv{0}
\PgInfo{part@8@2}{3}
\PgInfo{question8@object3}{3}
\newlabel{part@8@2}{{b}{3}{Problems}{Item.15}{}}
\PgInfo{question@9}{3}
\PgInfo{question9@object1}{3}
\newlabel{question@9}{{9}{3}{Problems}{Item.16}{}}
\PgInfo{question@10}{3}
\PgInfo{question10@object1}{3}
\newlabel{question@10}{{10}{3}{Problems}{Item.17}{}}
\PgInfo{question@11}{3}
\PgInfo{question11@object1}{3}
\newlabel{question@11}{{11}{3}{Problems}{Item.18}{}}
\PgInfo{question@12}{3}
\PgInfo{question12@object1}{3}
\newlabel{question@12}{{12}{3}{Problems}{Item.19}{}}
\PgInfo{question@13}{3}
\PgInfo{question13@object1}{3}
\newlabel{question@13}{{13}{3}{Problems}{Item.20}{}}
\PgInfo{question@14}{3}
\PgInfo{question14@object1}{3}
\newlabel{question@14}{{14}{3}{Problems}{Item.21}{}}
\gdef\pointsofq@xv{5}
\gdef\bonuspointsofq@xv{0}
\gdef\pointsofq@xvi{2}
\gdef\bonuspointsofq@xvi{0}
\gdef\pointsofq@xvii{2}
\gdef\bonuspointsofq@xvii{0}
\gdef\pointsofq@xviii{3}
\gdef\bonuspointsofq@xviii{0}
\gdef\pointsofq@xix{2}
\gdef\bonuspointsofq@xix{0}
\gdef\pointsofq@xx{2}
\gdef\bonuspointsofq@xx{0}
\PgInfo{question@15}{4}
\PgInfo{question15@object1}{4}
\newlabel{question@15}{{15}{4}{Problems}{Item.22}{}}
\PgInfo{part@15@1}{4}
\PgInfo{question15@object2}{4}
\newlabel{part@15@1}{{a}{4}{Problems}{Item.23}{}}
\PgInfo{part@15@2}{4}
\PgInfo{question15@object3}{4}
\newlabel{part@15@2}{{b}{4}{Problems}{Item.24}{}}
\PgInfo{question@16}{4}
\PgInfo{question16@object1}{4}
\newlabel{question@16}{{16}{4}{Problems}{Item.25}{}}
\PgInfo{question@17}{4}
\PgInfo{question17@object1}{4}
\newlabel{question@17}{{17}{4}{Problems}{Item.26}{}}
\PgInfo{question@18}{4}
\PgInfo{question18@object1}{4}
\newlabel{question@18}{{18}{4}{Problems}{Item.27}{}}
\PgInfo{question@19}{4}
\PgInfo{question19@object1}{4}
\newlabel{question@19}{{19}{4}{Problems}{Item.28}{}}
\PgInfo{question@20}{4}
\PgInfo{question20@object1}{4}
\newlabel{question@20}{{20}{4}{Problems}{Item.29}{}}
\gdef\pointsofq@xxi{2}
\gdef\bonuspointsofq@xxi{0}
\gdef\pointsofq@xxii{2}
\gdef\bonuspointsofq@xxii{0}
\PgInfo{question@21}{5}
\PgInfo{question21@object1}{5}
\newlabel{question@21}{{21}{5}{Problems}{Item.30}{}}
\PgInfo{question@22}{5}
\PgInfo{question22@object1}{5}
\newlabel{question@22}{{22}{5}{Problems}{Item.31}{}}
\gdef\exam@lastpage{6}
\gdef\exam@lastcoverpage{0}
\gdef\exam@totalpages{6}
\gdef\exam@numpoints{53}
\gdef\exam@numbonuspoints{0}
\gdef\exam@numquestions{22}
\gdef\exam@numparts{4}
\gdef\exam@numsubparts{0}
\gdef\exam@numsubsubparts{0}
\gdef\pointsonpage@ii{39}
\gdef\lastpage@withpoints{2}
\gdef\lastpage@withbonuspoints{0}
\gdef \@abspage@last{6}